derivative of sqrt(x+x^2)

Lösung

\frac{d}{d x} (x + x^{2})

\frac{1 + 2 x}{2 x + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x + x^{2})

Wende die Kettenregel an:

\frac{1}{2 x + x ^{2}} \frac{d}{d x} (x + x^{2})

= \frac{1}{2 x + x ^{2}} \frac{d}{d x} (x + x^{2})

\frac{d}{d x} (x + x^{2}) = 1 + 2 x

= \frac{1}{2 x + x ^{2}} (1 + 2 x)

Vereinfache

\frac{1}{2 x + x ^{2}} (1 + 2 x) : \frac{1 + 2 x}{2 x + x ^{2}}

= \frac{1 + 2 x}{2 x + x ^{2}}

in v erse l a pl a ce \frac{1}{s ^{2}} \cdot \frac{3}{( s + 1 )}

\int \frac{2 x + 1}{( x ^{2} + 4 ) ^{2} ( x + 1 ) ^{3}} d x

\frac{d}{d x} (x^{7} cos (x))

d er i v a t i v e \frac{u}{u ^{2} + 6}

\int \frac{( x ^{2} - 16 ) ^{\frac{3}{2}}}{x ^{3}} d x